login
Number of nonequivalent symmetric sets whose translations cover {1..n}.
1

%I #6 Nov 08 2019 18:14:39

%S 1,2,3,5,6,10,12,19,23,36,44,68,84,128,161,243,308,462,592,882,1140,

%T 1690,2200,3249,4255,6264,8246,12110,16008,23466,31128,45566,60618,

%U 88644,118205,172731,230782,337072,451082,658628,882582,1288432,1728484,2523104,3388084

%N Number of nonequivalent symmetric sets whose translations cover {1..n}.

%C Equivalence is up to translation. Only translations that are subsets of {1..n} are included.

%C Symmetric sets are those such that the set remains unchanged after mapping each element x to m - x, where m is the sum of the greatest and least elements. All sets of at most two elements are symmetric.

%e For n = 6 there are 10 symmetric sets (up to equivalence) that with their translations cover {1..6}:

%e {{1}, {2}, {3}, {4}, {5}, {6}};

%e {{1, 4}, {2, 5}, {3, 6}};

%e {{1, 3}, {2, 4}, {3, 5}, {4, 6}};

%e {{1, 3, 5}, {2, 4, 6}};

%e {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}};

%e {{1, 2, 4, 5}, {2, 3, 5, 6}};

%e {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}};

%e {{1, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}};

%e {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}};

%e {{1, 2, 3, 4, 5, 6}}.

%Y Cf. A079500 (if symmetry is not required).

%Y Cf. A096202, A329128.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Nov 08 2019